The increasing cost of happiness
R.W. Morris1,2, N. Kettlewell2,3,4 & N.Glozier1,5
- Central Clinical School, Faculty of Medicine and Health, University of Sydney, NSW, Australia
- ARC Centre of Excellence for Children and Families over the Life Course, University of Sydney, NSW, Australia
- School of Economics, University of Technology, NSW, Australia
- Institute of Labor Economics (IZA), Bonn, Germany
- Brain and Mind Centre, University of Sydney, NSW, Australia
Corresponding author:
Professor Nick Glozier
Faculty of Medicine and Health,
University of Sydney,
NSW 2050,
Australia
email: nick.glozier@sydney.edu.au
| Draft | 08 February, 2021 |
| Words | 4789 |
| Tables | 0 |
| Figures | 4 |
keywords: Subjective wellbeing, household income, HILDA
Abstract
A fundamental question for society is how much happiness does a dollar buy? The accepted view among economists and psychologists is that money and happiness increase together up to a point, after which there is little further gain from increasing wealth. While the location of this change point reportedly ranges between USD$60K to $95K, there has been no investigation as to whether this has increased or decreased over time. We tested the temporal relationship between income and affective wellbeing (happiness), and income and cognitive wellbeing (life satisfaction), using household economic data from Australia between 2002-2018. We discovered the change point between happiness and income has increased over those 17 years faster than inflation (i.e., cost of living). This suggests that inequalities in income may be driving increasing inequities in happiness between the rich and the poor, with implications for health and recent government policy-goals to monitor and improve wellbeing. (250 words max)
Significance Statement
Substantial research has shown that higher incomes have decreasing gains on wellbeing and happiness, across countries, cultures and ethnicities, with an inflection or change point at or near USD75,000. At incomes below this point happiness is dependent on financial security while at income levels above, happiness is relatively independent; revealing an inequality in the distribution of happiness between rich and poor. However we do not know whether or how this point has itself changed over time. Has it decreased and reduced inequality, or increased the difference between the rich and poor? We examine 17 years of data from a single developed western nation (Australia) and determine that the happiness of more people are dependent on financial security than before.
Background
A fundamental question for governments and people is just how much wellbeing does a dollar buy? Increasing income is commonly associated with increasing happiness and wellbeing, however a point at which subjective wellbeing no longer increases with income has also been widely observed (Clark et al., 2008; Dolan et al., 2008; Easterlin, 1974). Given that a central goal of nations and governments is to improve income under the assumption that higher income always increases wellbeing, challenges to this notion have far reaching consequences (Frijters et al., 2020; Laws and Monitor, 2014).
Subjective wellbeing is not a unitary entity (Diener et al., 2017); studies typically distinguish between life satisfaction, the cognitive appraisal of one’s own accomplishments, and affective wellbeing, one’s prevailing affective state, emotional mood, or everyday experience of happiness. Money can have different effects on each. For instance, we have recently reported that large increases in wealth, such as a major financial windfall, have a greater impact on an individual’s life satisfaction than their happiness (Kettlewell et al., 2020). The distinct effect of money on satisfaction and happiness was observed within an individual over time, however a distinct effect of income have also been observed between people with different income levels. For instance, Kahneman & Deaton (2010) showed that self-reported levels of happiness increased with household income up to a point (USD75,000), but after that, increasing income had little further effect on happiness. Conversely life satisfaction continued to increase with income beyond USD75,000. Indeed, the difference between the two questions: “How satisfied are you with your life?” and “How happy are you these days?” has been identified as a crucial mediating factor in a meta-analysis of 111 studies on income and wellbeing (Howell and Howell, 2008; also Veenhoven and Hagerty, 2006). Results such as these have provided a more nuanced view among psychologists and some economists regarding the relationship between income and wellbeing; namely that income is more strongly related to satisfaction than to happiness.
Fundamentally, the existence of a change point in the relationship between income and happiness reveals an unacknowledged source of inequality in the distribution of wellbeing (i.e., happiness) in the economy. For instance, the change point of USD75,000 reported by Kahneman in 2008 was substantially more than the US median income of USD52,000 in the same year, indicating that the happiness of the poorest majority of the US population was tied to marginal changes in income while the happiness of a richer minority was not. Thus the change point represents the dollar value up to which income drives inequities in the distribution of happiness, such that a lower value represents a more equitable distribution of happiness in the economy. Inequities in the distribution of wellbeing are increasingly relevant to governments and policy-makers due to the growing recognition that increasing income does not necessarily lead to equal changes in wellbeing (Clark, 2018; Frijters et al., 2020). Even prior to COVID-19, the World Gallup Poll has observed that happiness has been decreasing over the past decade in western Europe, north America, Australia and New Zealand, despite increases in income in the same countries (Sachs et al., 2019). However to date there has been no investigation of whether the relationship between income and happiness has changed over time which may contribute to these social trends. In particular has the change point between income and happiness, and therefore the distribution of happiness between rich and poor, become more or less equitable in the last few decades?
Methods
We used household economic panel data from Australia (HILDA) to provide the first investigation of whether changes in income and wellbeing have shifted the change point over the last 17 years (2002-2018). HILDA provides a representative sample of households in Australia with detailed measurements of income and subjective wellbeing in the same sample, which makes it an excellent data source to investigate the present question. We distinguished between satisfaction and happiness as different components of subjective wellbeing, and evaluated how each varies with household income. Full-time students were removed, as well as individuals with an annual household disposable income designated as topcoded (which occurs to ensure confidentiality of very high income individuals who might otherwise be identifiable).
Income
To allow comparison with other major studies of income and wellbeing we used household after-tax income as the indicator of income and economic security (e..g, Kahneman and Deaton, 2010; Jebb et al., 2018). Household income better represents economic security than personal income, since members of the same household share expenses as well as risks; i.e., they can provide a direct and immediate support network when financial shocks occur, which a priori might affect wellbeing. The ‘real household annual disposable income’ was calculated from the self-reported combined income of all household members after receipt of government pensions and benefits and deduction of income taxes in the financial year ended 30th June of the year of the wave (e.g., 2002 in wave 2). This was then adjusted for inflation - the rise in the general price level of the economy - using the Australian Bureau of Statistics (ABS) Consumer Price Index, so that income in all waves is expressed in FY 2017/18 prices, to give real income.
The equivalised household income was obtained by adjusting for household size (the number of adult and child household members). In this instance, we have used the ‘modified OECD’ scale (Hagenaars et al., 1994), which divides household income by 1 for the first household member plus 0.5 for each other household member aged 15 or over, plus 0.3 for each child under 15. A family comprising two adults and two children under 15 years of age would therefore have an equivalence scale of 2.1 (1 + 0.5 + 0.3 + 0.3), meaning that the family would need to have an income 2.1 times that of a single-person household in order to achieve the same standard of living. This scale recognises that larger households require more income, but it also recognises that there are economies of scale in consumption and that children require less than adults. The equivalised income calculated for a household is then assigned to each member of the household.
Subjective Wellbeing
There are a variety of variables related to subjective well-being collected annually in HILDA, but the two we used here matched the variables we used in our previous paper (Kettlewell et al., 2020), namely, life satisfaction as a measure of cognitive wellbeing, and item 9 from the SF-36 (9a-9i) as a measure of affective wellbeing or happiness.
Life satisfaction (losat) was assessed by a single item question asked each survey: “All things considered, how satisfied are you with your life (0 to 10)”.
Happiness was determined by 9 questions in the SF-36 (9a to 9i). The SF-36 is a widely used self-completion measure of various aspects of physical, emotional and mental health (Ware Jr, 2000). A subset of 9 questions assess mental health and vitality, with five questions measuring positive and negative aspects of mental health (e.g., “Felt so down in the dumps nothing could cheer me up”, “Been happy”), and four questions on positive and negative aspects of vitality (e.g., “feel full of life”, “felt worn out”). The response scale timeframe is the past four weeks and agreement was indicated on a six-point Likert scale. We reverse scored negatively phrased questions and calculated the sum of the nine questions so that higher scores represented better wellbeing. To aid interpretability, we rescaled the final sum to a score between 1-100, where 100 represents the maximum happiness achievable.
For modelling, both dependent variables were rescaled with a mean of zero and a SD of 1 (z-scores) for each year.
Modelling
We modelled the relationship between income and each wellbeing variable (happiness and satisfaction) using a simple linear model and a piecewise model (broken-stick). The piecewise model was chosen as the simplest extension of a linear model which can identify a change point (inflection) in the relationship between wellbeing and income. The location of the change point was a free parameter which revealed where wellbeing no longer increased at a uniform rate with income. We then compared the linear model against the piecewise model to determine if a change point existed in any year between household income and each wellbeing variable (see Model Selection). Finally, where a change point existed, we determined the location of the change point for that year (see Parameter Estimation).
For modelling, both measures of wellbeing were rescaled with a mean of zero and a SD of 1 (z-scores) for each year.
Model Estimation
We adopted a Bayesian approach for estimating the linear and piecewise model in the software Stan (Bürkner, 2017; Stan Development Team, 2019). In each case the linear model was estimated as:
\[ y_i \sim N(\mu_i, \sigma^2_y) \]
\[ \mu_i = \beta_0 + \beta_1 X_i \]
Where \(X_i\) was an individual’s household income ($) as well as other covariates (age, age2, sex, education), and \(y_i\) was an individual’s wellbeing.
The piecewise model was a simple extension of this to include a free parameter to represent the changepoint in income (\(\omega\)) as well as the slope before the change point (\(\beta_1\)) and the slope after the change point (\(\beta_2\)):
\[ \mu_i = \beta_0 + \beta_1 (x_i - \omega) (x_i ≤ \omega) + \beta_2 (x_i - \omega) (x_i > \omega) + \beta_3 X_i \]
Where \(x_i\) was an individual’s household income, and \(X_i\) were covariates for age, age2, sex and education.
The above models estimated population-level effects separately for each year (t = 2002…2018). Because we were interested in the location of the change point between income and wellbeing that existed across individuals within each year, we ignored the panel design of HILDA because the dependency between observations of the same person across years was orthogonal to our effects of interest. We specified weakly informed priors for each β, and a uniform prior over the restricted range of income values for ω.
Model Selection
To determine whether wellbeing was a linear or non-linear (e.g., piecewise) function of income, we compared the linear and piecewise model posterior probabilities using the Widely Applicable Information Criterion (WAIC). The WAIC is the log-posterior predictive density plus a penalty proportional to the variance in the posterior distribution. Thus it provides an approximation of the out-of-sample deviance that converges to the cross-validation approximation in a large sample, with a penalty for the effective number of parameters (degrees of freedom). For this reason is it useful to compare two models of varying complexity, such as our linear and piecewise model.
WAIC was defined as: WAIC = -2(lppd - pWAIC)
Where lppd (log pointwise predictive density) is the total across observations of the log of the average likelihood of each observation, and pWAIC is the effective number of free parameters determined by the sum of the variance in log-likelihood for each observation (i).
Parameter Estimation
To determine the location of the change point (ω) between wellbeing and income, we modelled the relationship between income and wellbeing across individuals using the piecewise model described above, and sampled the posterior probability of ω over 4000 interations. The complete posterior distribution of ω for each year is presented along with the expected value (mean).
Covariates
Age (and age2), gender, and university graduate education were included as covariates. Cross-sectional population weights for Australia provided by the University of Melbourne for each year were also included as a covariate to adjust for differences in the sample representativeness according to sex by broad age, marital status, region, and labour force status. Full-time students were removed, as well as individuals with an annual household disposable income that was indicated as topcoded by the University of Melbourne (topcoding occurs to ensure privacy of high wealth individuals). Gender was included as a binary variable (Male = 1), and education was a binary variable coded from the highest level of education achieved (university/college graduate = 1).
Results
The broad demographic characteristics of the sample are presented in Supplementary Materials Table S1. Average life satisfaction levels were very steady between 2002-2018, while average happiness score decreased slightly over the 17 years. The proportions of each sex and relationship status were stable over time, as were the average household size and SEIFA index. However age, education, and chronic health conditions tended to slightly increase over time. For instance, average age increased by 1.8 years over the 17 years of the survey, which is obviously less than would occur in a cohort study (Watson and Wooden, 2012). Changes in the workforce varied with economic circumstances.
Happiness and satisfaction have distinct relationships with income
The relationship between household income and happiness (red) and satisfaction (blue) every four years is shown in Figure 1. For each wellbeing variable we show the results of a linear fit (rows 1 and 3) and a piecewise fit (rows 2 and 4). For visualization purposes only, due to the large numbers of individual data in each year, we display the mean levels of income and wellbeing for each (equal-sized) income decile rather than every individual data point, whereas the line-of-best-fit and 95% credible intervals (shaded) in each regression model are derived from all individuals.
Figure 1. Household income and happiness (red) and satisfaction (blue)
Figure 1 legend: The relationship between income and wellbeing across equal-sized income deciles, overlaid by regression lines from linear and piecewise models (±95%CI). Wellbeing was measured as happiness (red) or life satisfaction (blue). The total number of individuals contributing to each regression in each year are noted (n).The nonlinear relationship between happiness and income (Figure 1, 2nd row) was consistently and negatively inflected (happiness increased less with income after the change point). By contrast the nonlinear relationship between satisfaction and income shown in the 4th row was as likely to be negatively inflected as positively inflected: positively inflected in 2002 and 2006; negatively inflected 2014 and 2018; and no apparent inflection in 2010.
The posterior evidence from model selection revealed the nonlinear (piecewise) fit of happiness, but not satisfaction, was credibly superior to a linear fit in each year (Supplementary Materials, Figure S2). Overall the posterior evidence suggests that happiness and satisfaction have distinct relationships with household income; satisfaction tends to increase linearly with income, while a change point exists in the relationship between happiness and household income.
The evolution of income on happiness 2002-2018
Figure 2 below presents the posterior distribution of each parameter from the piecewise model regressing happiness on income: the change point (ω), the intercept (β0), the pre-change slope (β1), and the post-change slope (β2). Over 12,000 samples were drawn from each piecewise model to determine the posterior distribution of each parameter. Horizontal bars represent the 95% credible interval and so intervals which fall completely to the right of the vertical grey dotted line are credibly higher than our base year 2002.
Figure 2. Posterior parameters of income on happiness
Figure 2 legend: Posterior distributions of the change point parameter omega representing the location in real household income (2018 dollars), as well as the intercept, preslope and postslope parameters in arbitrary units. Horizontal bar represents the 95% credible region and the solid point indicates the expected value (median) of each distribution. Vertical dotted line indicates the 2002 parameter value (median) as a base year comparison.The posterior estimates of the change point between happiness and household income indicates that the location (i.e., the real income value) of the change point shows a systematic increasing trend since 2011. Changes to the other parameters of the function between income and happiness also occured between 2002 and 2018 (i.e., the pre-slope, post-slope and intercept), however these did not show any sustained trend over the period nor result in a reliable change from the baseline year 2002.
It is also worth noting that both the pre-slope and post-slope parameters (β1 and β2) were credibly larger than zero in most years, indicating there was a reliable dependency between happiness and income at income levels below and above the change point. However comparing the pre-slope with the post-slope values makes clear that the relationship between happiness and income among the majority of people in lower income households was an order of magnitude steeper than those in high income households.
The change in parameter values between 2002 to 2018 indicates the relationship between happiness and income evolved over time. We determined the impact of this evolution on the distribution of happiness over the range of household income in 2018 in a counterfactual analysis. The counterfactual analysis is a hypothetical demonstration of how happiness would change if people in 2018 were subject to the function that existed in 2002. That is, would happiness increase or decrease if the 2002 function was in place in 2018? It controls for changes in the sample which occur over time that are not related to happiness but could nevertheless contribute to changes in the distribution of happiness. For example, the increase in the range of (real) income levels in the economy between 2002 and 2018 could produce a greater divergence in happiness due to the increasing gap between the rich and poor - even with a stable relationship between income and happiness. Such changes in the sample characteristics may mask or confound the impact of the change point on the distribution of happiness without careful control. Because we were interested in the implications of the evolution of the function rather than changes in our sample characteristics per se, we estimated happiness levels for each n = 14,280 person in 2018 using the 2002 function. These 2002 model-estimates were compared to (subtracted from) the 2018 model-estimates generated from the same sample (n = 14,280), to obtain the change (delta) in happiness for each person under the counterfactual. This delta must be entirely due to the evolution of the function between 2002 and 2018, since the analysis has held everything else constant (i.e., exactly the same people with the same characteristics were used to estimate happiness from two different functions). Figure 3 below presents the 14,280 deltas from such a comparison, along with a smoothed mean (blue overlay) to summarize how happiness evolved with the function across the entire income distribution.
Figure 3. Counterfactual difference in happiness between 2002 and 2018
Figure 3 legend: The difference (∆) in model-estimated happiness between 2018 and 2002 for the same n = 14,280 individuals from the 2018 survey. Values below zero on the y-axis indicate lower happiness estimates in 2018 relative to 2002. Points to the left of the vertial ($72K) are individuals below the 2018 change point. The smoothed overlay (blue) indicates how the average delta changes across the income distribution. Figure 3 shows that, on average, happiness estimates improved for people with household incomes above $72K when compared to 2002, as indicated by the average delta (smooth blue line) falling above zero on the right side of the plot. Conversely, people with household incomes below $72K, on average, suffered a decrease in estimated happiness compared to 2002. And the greatest decrease in happiness occurred for people whose income levels were transliminal: that is, their income was above the changepoint in 2002 but the shift in the change point resulted in their income falling below the change point in 2018. Of course the obtained deltas are due to changes in all the parameters of the function, including the slope before and after the change point. However because this comparison was performed on the same individuals (i.e., from the 2018 survey), it held characteristics such as age, income, etc, constant that would otherwise be expected to change over time and possibly contribute to any difference in happiness distribution. In this way these results isolate the amount of change entirely due to the evolution of the function between 2002 and 2018, and demonstrates how this has contributed to the unequal distribution of happiness between the rich and the poor over time.
The increasing cost of happiness in Australia
A less hypothetical implication of the shifting change point in the relationship between income and happiness is that over time fewer people have an income that affords them happiness, which is (relatively) independent of their financial security. Assuming median income is also not increasing at a faster rate, any increase in the change point will reduce the number of people who fall above it over time. Figure 5 presents median household income levels weighted for the Australian population (by age, sex, marital status, labour force participation and geographical region). It also shows the change point between income and happiness increased faster than rises in median household income between 2002 and 2018. The third panel shows that as a result, a smaller proportion of the Australian population in 2018 had a household income above the changepoint than in 2002.
Figure 4. Rise in median income, change point, and population in Australia 2002-2018
Figure 4 legend: Real household income has stagnated in Australia since 2009 (post GFC) while the change point between happiness and income has increased. Consequently fewer Australians had an income that affords them happiness, which is independent of their financial security in 2018.Conclusions
We confirmed previous findings (e.g., Howell and Howell, 2008; Kahneman and Deaton, 2010), that the relationship between both types of subjective wellbeing with household income was positive but quite different over a 17 year period: Satisfaction increased linearly with income, while happiness increased rapidly up to a point after which higher levels of income were associated with less improvement. For the first time we have shown that this change point in the relationship between household income and happiness increased faster than inflation or the median household income over time between 2002 and 2018.
We refer to the change point after which increases in income no longer produce similar increases in happiness as the cost of happiness. After this point, happiness is no longer as dependent on household income, and the economic security it represents. Presumably after this point further increases in happiness depend more on other life factors (e.g., leisure time, social connections). Life satisfaction on the other hand appeared to show consistent increases with household income and we found no evidence of any change point. The difference may reflect the importance of a numerical dollar value (e.g., bank balance, house value) when cognitively appraising one’s life achievements, versus the relevance of that number to our everyday experience of joy and our prevailing mood.
An implication of the changing relationship between happiness and income since 2002 is that income inequality may be driving increasing inequities in wellbeing. This is demonstrated in Figure 3, where the difference in happiness between 2002 and 2018 increased for incomes above $72K/year and decreased for incomes below that level. The inequity was also highlighted in Figure 4 where the change point of happiness represented a 9% increase over median income in 2002, while in 2018 it represented a 42% increase over median income. This increase relative to median income also represented a reduction from 42% to 24% in the proportion of people whose income fell above the changepoint. Thus we can see that over the last sixteen years the difference in happiness between the rich and the poor has increased; while the proportion of people whose happiness no longer depends on their financial security has decreased.
Australia has low levels of income disparity relative to many other OECD countries, and the Gini coefficient has not changed a great deal between 2002 and 2018 (APC and others, 2018). A stable Gini coefficient shows income inequality has remained steady over the time period, and our results do not conflict with this conclusion. Rather what we are revealing is that even a static income distribution may have dynamic effects on happiness over time. We think this highlights the issue that while traditional measures of wealth and income inequality may be relatively stable and exhibit little change, their impact on wellbeing and health can still vary. As such, we believe these results may well have relevance to other developed nations in North America and Europe which have enjoyed stable economic growth overall, but have stagnating incomes, and declining happiness levels (Sachs et al., 2019). As focus shifts from traditional financial indicators towards health and wellbeing measures, findings such as this may become more prevalent.
Some recent studies have challenged either the notion that the positive effect of income plateaus after some level, or that the effect on happiness and satisfaction are distinct (Jebb et al., 2018; Killingsworth, 2021; Twenge and Cooper, 2020). Most recently the point has been made that experienced happiness continues to increase on a log scale with income and does not plateau after USD75,000 (Killingsworth, 2021). It is worth noting that log-linear models are typically used to investigate income effects, and we would agree that our data do not support a strict view of a “satiety” point or flat gradient between income and happiness which can persist on a log scale [Jebb et al. (2018); kahneman2010high]. But log-linear models mask the fact that marginal dollars matter less the more one earns, which is what we observed for happiness here. Furthermore, log models (and more flexible additive models Jebb et al., 2018) may produce a better fit, but will not provide a clear or a distinct change point allowing us to test a change in the marginal effect of income. And so one implication of our model choice is that the change in slope may be much smoother than implied by our model. We concede this point but would still contend the location of the change in slope will display a comparable shift over time, if it can be detected with certainty.
Past researchers have also argued there is no distinct relationship between income and the different forms of subjective wellbeing (e.g., happiness, satisfaction), and that income has the same impact on both constructs. It is rare for such research to directly test differences in the form of the function, usually instead inferring no difference after observing null results. One benefit of our model selection was the quantification of the posterior evidence for a linear over a nonlinear function (e.g., Figure S1, Supplementary Materials). That showed the evidence for a linear effect was clearly different between our two wellbeing variables, and the evidence for a linear function was also decreasing over time. It may be that with more recent data, or in the near future, there is no distinct function between income and the different wellbeing constructs. However it is also worth noting that the only meta-analysis conducted in this area, over ten years ago, also suggested the linear relationship between income and life satisfaction is stronger than that with happiness (Howell and Howell, 2008). We would also note that a linear function between income and life satisfaction as we report here, is consistent with the majority of earlier research (Stevenson and Wolfers, 2013). In general, the importance of differences between the distinct constructs of subjective wellbeing will need to be adjudicated when deciding how to measure income effects.
As governments and policy-makers begin to focus on wellbeing, it will be critical to understand how traditional economic indicators such as household income, wealth inequality, and consumption interact with wellbeing and health. According to Frijters et al. (2020), coming up with a consensus to translate income into wellbeing features high on the wider wellbeing research agenda. Establishing the links between wealth, household income, wellbeing and health, and how inequalities in one drives inequities in the other, will be a critical step in the success of that agenda.
Acknowledgements
This research was not supported by any funding.
Competing interests
The authors declare no competing interests.
Additional information
This paper uses unit record data from Household, Income and Labour Dynamics in Australia Survey HILDA conducted by the Australian Government Department of Social Services (DSS). The findings and views reported in this paper, however, are those of the author[s] and should not be attributed to the Australian Government, DSS, or any of DSS’ contractors or partners. All code and scripts used in the analysis are available at https://github.com/datarichard/The-increasing-cost-of-happiness
Supplementary information is available here
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